Please solve the following discrete math problem: Write the negation of the following statement. (You can write "epsilon" for € and "delta" for8.)For every positive number e, there is a positive number 8 such that |x − a| < 8 implies |ƒ(x) —f(a) < €.Write the negation of the following statement.For every prime number p, there is another prime number 9 with q> p.

(i) For every positive number , there is a positive number such that implies .(ii) For every prime…

Answered: Write the negation of the following…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Please solve the following discrete math problem:

Write the negation of the following statement. (You can write "epsilon" for € and "delta" for
8.)
For every positive number e, there is a positive number 8 such that |x − a| < 8 implies |ƒ(x) —
f(a) < €.
Write the negation of the following statement.
For every prime number p, there is another prime number 9 with q> p.

Expert Solution

Step 1: Given the statements

(i) For every positive number $epsilon$ , there is a positive number $delta$ such that $open vertical bar x minus a close vertical bar less than delta$ implies $open vertical bar f left parenthesis x right parenthesis minus f left parenthesis a right parenthesis close vertical bar less than epsilon$ .

(ii) For every prime $p$ , there is another prime $q$ with $q greater than p$ .

The aim is to find the negation of each statement.